Navigation through polygonal no fly zones

ABSTRACT

An unmanned aerial vehicle (“UAV”) receives location information describing geographic boundaries of a polygonal no-fly zone (“NFZ”), the NFZ having a plurality of virtual walls each associated with a geographic line segment. The UAV identifies a closest and a second closest virtual wall of the plurality of virtual walls of the NFZ to a geographic location of the UAV. The UAV determines a first distance from the location of the UAV to a portion of the closest virtual wall nearest to the location of the UAV and a second distance from the location of the UAV to a portion of the second closest virtual wall nearest to the location of the UAV. In response to the first and/or second determined distances being less than a threshold distance, the UAV modifies a velocity and/or a trajectory of the UAV such that the UAV does not cross the virtual walls.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.62/411,611, filed Oct. 23, 2016, and U.S. Provisional Application No.62/411,612, filed Oct. 23, 2016, both of which are incorporated hereinby reference in their entirety.

BACKGROUND Field of Art

The disclosure generally relates to the field of remote controlledaerial vehicles, and in particular to the navigation of aerial vehiclesin proximity to virtual walls and no-fly zones.

Description of Art

Unmanned aerial vehicles (or “UAVs” hereinafter) continue to grow inpopularity for both their commercial applications as well asrecreational uses by hobbyists. The ability of remote controlled aerialvehicles to quickly traverse space and to access places which a usercannot provides for many useful applications. However, a remotecontrolled aerial vehicle must, in general, avoid flying into prohibitedareas, for example high-security areas, private property areas, areas inwhich flying presents a possible danger, and the like (collectivelyreferred to herein as “no-fly zones” or “NFZs”).

The boundaries of an NFZ can be defined in advance, for instancerelative to a map. Each segment of an NFZ boundary can be referred to asa “virtual wall”, through which the UAV should be prevented from flying.A user navigating a UAV may not be able to see a boundary of an NFZ, ormay not be aware of the existence of an NFZ. Accordingly, there is aneed for the UAV to be able to navigate around or otherwise avoidcrossing an NFZ threshold or virtual wall without requiring the explicitactions or input from a user.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosed embodiments have advantages and features which will bemore readily apparent from the detailed description, the appendedclaims, and the accompanying figures (or drawings). A brief introductionof the figures is below.

Figure (FIG. 1 is an example of a remote controlled aerial vehicle incommunication with a remote controller.

FIG. 2 illustrates an example of a remote controlled aerial vehicle.

FIG. 3 illustrates an example of a remote controller.

FIG. 4A illustrates an example of a remote controlled aerial vehicleelectronics and control systems.

FIG. 4B illustrates an example interconnect architecture of a remotecontrolled aerial vehicle with a gimbal.

FIG. 5 is a high-level block diagram illustrating a flight controller,in accordance with one embodiment.

FIG. 6 is a flow chart of a process for determining distances from theset point of a remote controlled aerial vehicle to two virtual walls ofa NFZ, in accordance with an embodiment.

FIG. 7 illustrates three examples in which a remote controlled aerialvehicle approaches a polygonal NFZ, in accordance with one embodiment.

FIG. 8 is a flow chart of a process for modifying the movement of theset point of a remote controlled aerial vehicle, in accordance with anembodiment.

FIG. 9A illustrates a free-sliding mode of operation used by a remotecontrolled aerial vehicle to navigate the area surrounding a NFZ, inaccordance with one embodiment.

FIG. 9B illustrates a restricted-sliding mode of operation used by anaerial vehicle operating in part under remote control to navigate thearea surrounding a NFZ, in accordance with one embodiment.

FIG. 9C illustrates a non-sliding mode of operation used by a remotecontrolled aerial vehicle to navigate the area surrounding a NFZ, inaccordance with one embodiment.

DETAILED DESCRIPTION

The Figures (FIGS.) and the following description relate to preferredembodiments by way of illustration only. It should be noted that fromthe following discussion, alternative embodiments of the structures andmethods disclosed herein will be readily recognized as viablealternatives that may be employed without departing from the principlesof what is claimed.

Reference will now be made in detail to several embodiments, examples ofwhich are illustrated in the accompanying figures. It is noted thatwherever practicable similar or like reference numbers may be used inthe figures and may indicate similar or like functionality. The figuresdepict embodiments of the disclosed system (or method) for purposes ofillustration only. One skilled in the art will readily recognize fromthe following description that alternative embodiments of the structuresand methods illustrated herein may be employed without departing fromthe principles described herein.

Example Aerial Vehicle Configuration

Figure (FIG. 1 illustrates an example embodiment in which an aerialvehicle 110 is a quadcopter (i.e., a helicopter with four rotors). Theaerial vehicle 110 in this example includes a housing 130 for payload(e.g., electronics, storage media, and/or camera), four arms 135, fourrotors 140, and four propellers 145. Each arm 135 may mechanicallycouple with a rotor 140 to create a rotary assembly. When the rotaryassembly is operational, all the propellers 145 may spin at appropriatespeeds to allow the aerial vehicle 110 lift (take off), land, hover,move, and rotate in flight. Modulation of the power supplied to each ofthe rotors 140 may control the acceleration and torque on the aerialvehicle 110.

A gimbal 175 may be coupled to the housing 130 of the aerial vehicle 110through a removable coupling mechanism that mates with a reciprocalmechanism on the aerial vehicle 110. The coupling between the gimbal 175and the aerial vehicle 110 may have mechanical and communicativecapabilities. In some embodiments, the gimbal 175 may be attached orremoved from the aerial vehicle 110 without the use of tools. A camera115 may be mechanically coupled to the gimbal 175, so that the gimbal175 steadies and controls the orientation of the camera 115. It is notedthat in alternate embodiments, the camera 115 and the gimbal 175 may bean integrated configuration.

The aerial vehicle 110 may communicate with a device via a wirelessnetwork 125. The device that communicates with the aerial vehicle 110 isdescribed herein as being a remote controller 120. However, in alternateembodiments, the device may be any other computing device capable ofwireless communicating (e.g., transmitting, receiving, or both) with theaerial vehicle 110. Some or all of the description attributed herein tothe remote controller 120 may also be applied to other computing devicescapable of wireless communication. Other computing devices may include adevice with a screen that is used to display images or video captured bythe aerial vehicle but not to control the aerial vehicle, such as, alaptop, smartphone, tablet, or head-mounted display.

In one embodiment, the wireless network 125 may be a long range Wi-Fisystem. It also may include or be another wireless communication system,for example, one based on long term evolution (LTE), 3G, 4G, or 5Gmobile communication standards. In some embodiments, the wirelessnetwork 125 consists of a single channel and the aerial vehicle 110 andthe remote controller 120 implement a half-duplex system. In analternate embodiment, the wireless network 125 includes two channels: aunidirectional channel used for communication of control informationfrom the remote controller 120 to the aerial vehicle 110 and a separateunidirectional channel used for video downlink from the aerial vehicle110 to the remote controller 120 (or to another device, such as a videoreceiver where direct video connection may be desired). Alternatewireless network configurations may also be used.

The remote controller 120 in this example includes a first control panel150, a second control panel 155, an ignition button 160, a return button165, and a screen (or display) 170. One primary purpose of the remotecontroller 120 is to facilitate movement of the aerial vehicle 110. Tofacilitate such movement, the remote controller 120 directs movement ofa set point of the aerial vehicle 110. The set point of the aerialvehicle 110 is a mobile point in space that the aerial vehicle 110attempts to reach through movement. The location, speed, and trajectoryof the set point can be changed via instructions from a flightcontroller 402. When the aerial vehicle 110 reaches the set point, ithovers at that point until the location of the set point is changed viainstructions from the flight controller 402. Following the change inlocation of the set point, the aerial vehicle 110 again moves towardsthe updated location of the set point. Thus movement of the set point ofthe aerial vehicle 110 informs movement of the aerial vehicle 110itself. Specifically, movement of the set point of the aerial vehicle110 designates the speed, direction, and trajectory of the aerialvehicle 110.

As previously mentioned, the set point of the aerial vehicle 110 ischanged via input to the flight controller 120. The first control panel150 of flight controller 120 may be used to control “up-down” direction(e.g. lift and landing) of the set point of the aerial vehicle 110. Thesecond control panel 155 may be used to control “forward-reverse” or maycontrol the direction of the set point of the aerial vehicle 110. Inalternate embodiments, the control panels 150, 155 are mapped todifferent directions for the aerial vehicle 110. Each control panel 150,155 may be structurally configured as a joystick controller and/or touchpad controller. The ignition button 160 may be used to start the rotaryassembly (e.g., start the propellers 145). The return button 165 may beused to override the controls of the remote controller 120 and transmitinstructions to the aerial vehicle 110 to autonomously return to apredefined location. The ignition button 260 and the return button 265may be mechanical and/or solid state press sensitive buttons.

In addition, each button may be illuminated with one or more lightemitting diodes (LEDs) to provide additional details. For example a LEDmay switch from one visual state to another to indicate with respect tothe ignition button 160 whether the aerial vehicle 110 is ready to fly(e.g., lit green) or not (e.g., lit red) or whether the aerial vehicle110 is now in an override mode on return path (e.g., lit yellow) or not(e.g., lit red). It also is noted that the remote controller 120 mayinclude other dedicated hardware buttons and switches and those buttonsand switches may be solid state buttons and switches. For example, abutton or switch may be configured to allow for triggering a signal tothe aerial vehicle 110 to immediately execute a landing operation.

The remote controller 120 may also include hardware buttons or othercontrols that control the gimbal 175 or camera 115. The remotecontroller 120 may allow it's user to change the preferred orientationof the camera 115. In some embodiments, the preferred orientation of thecamera 115 may be set relative to the angle of the aerial vehicle 110.In another embodiment, the preferred orientation of the camera 115 maybe set relative to the ground. The remote controller 120 may alsotransmit commands to the aerial vehicle 110 which are routed to thecamera 115 through the gimbal 175 to take a picture, record a video,change a picture or video setting, and the like.

The remote controller 120 also may include a screen 170 which providesfor visual display. The screen 170 may be a touch sensitive screen. Thescreen 170 also may be, for example, a liquid crystal display (LCD), anLED display, an organic LED (OLED) display, or a plasma screen. Thescreen 170 may allow for display of information related to the remotecontroller 120, such as menus for configuring the remote controller 120or remotely configuring the aerial vehicle 110. The screen 170 also maydisplay images or video captured from the camera 115 coupled with theaerial vehicle 110, wherein the images and video are transmitted to theremote controller 120 via the wireless network 125. The video contentdisplayed on the screen 170 may be a live feed of the video or a portionof the video captured by the camera 115. It is noted that the videocontent may be displayed on the screen 170 within a short time (e.g.,within fractions of a second) of being captured by the camera 115. Thedelay between the video being captured by the camera 115 and beingdisplayed on the screen 170 may be instantaneous or nearly instantaneousin terms of human perceptual quality.

The remote controller 120 shown in FIG. 1 is a dedicated remotecontroller, but in alternate embodiments the remote controller may beanother computing device such as a laptop, smartphone, or tablet that isconfigured to wirelessly communicate directly through an antenna systemwith the aerial vehicle 110 to control the aerial vehicle 110.

FIG. 2 illustrates an example of an aerial vehicle 110. The aerialvehicle 110 may be coupled to a camera 115 via a gimbal 175. The camera115 may capture video and send the video to the aerial vehicle 110through a bus of the gimbal 175. The aerial vehicle 110 may wirelesslytransmit the video to the remote controller 120. The aerial vehicle 110may include one or more internal antennas in the housing 130 fortransmitting signals to and receiving signals from the remote controller120. The one or more antennas may be omnidirectional. In someembodiments, the antennas of the aerial vehicle 110 radiate the majorityof their power beneath the aerial vehicle 110 (e.g., in the semi-spherebeneath the aerial vehicle 110).

FIG. 3 illustrates an example of a remote controller 120. The remotecontroller 120 may communicatively couple with the aerial vehicle 110,for example, via a wireless communication protocol such as Wi-Fi. Theremote controller 120 may include a first section 330 and a secondsection 340 which may fold together via a hinge 350 connecting the twosections. The first section 330 may include a first control panel 150, asecond control panel 155, an ignition button 160, a return button 165, apower button 310, and a speaker 320. The first section 330 also mayinclude a housing containing electronics, such as processors andantennas. The second section 340 may include a screen 170. The hinge 350may allow the first section 330 and second section 340 to rotaterelative to each other. The hinge 350 may include one or more cams(e.g., v-cams) so that the hinge 350 may fix the rotation of the firstsection 340 and second section 340 to a finite number of angles. Forexample, the hinge 350 may be fixed at a 0° rotation (i.e., where theremote controller 120 is closed), a 90° rotation (i.e., where the screen170 is perpendicular to the face of the first section 330), and 170°rotation (as shown in FIG. 3). In some embodiments, the hinge 350 may bean adjustable friction hinge so that the user can adjust the relativeorientation of the first section 330 and the second section 340.

The remote controller 120 may include a screen 170 and a speaker 320(e.g., an electroacoustic transducer) for providing output to a user.The speaker 320 may output sound from a video as it is displayed on thescreen 170. The video may be received from the aerial vehicle 110 viathe wireless network 125. The speaker 320 may also output soundsresponsive to the user pressing a button or as an alert to the user. Forexample, the speaker may output an alert when the battery of the aerialvehicle 110 is nearly depleted, when an error is detected on the aerialvehicle 110 (e.g., a mechanical malfunction, a software error, anelectronic malfunction, or a combination thereof), when the signalstrength between the aerial vehicle 110 and the remote controller 120 isweak, when the antenna of the remote controller 120 is not orientedcorrectly, and/or when the wireless connection with the aerial vehicle110 is lost. As another example, when one or more components of flightbehavior of the aerial vehicle 110 such as trajectory or speed has beenaltered, the speaker 320 may output an audio alert describing thealteration in flight behavior and the screen 170 may display a visualalert providing similar information. The speaker 320 may also output analert to indicate to the user that the aerial vehicle 110 is in closeproximity to, or entering, a no-fly zone (NFZ). Furthermore, the screen170 may display a visual warning indicating to the user that the aerialvehicle 110 is in close proximity to, or entering a NFZ.

The remote controller 120 also includes user input devices.Specifically, the remote controller 120 may include a first controlpanel 150, a second control panel 155, an ignition button 160, a returnbutton 165, and a power button 310. The first control panel 150 and thesecond control panel, 155 may be joystick controllers for controllingthe velocity and orientation of the aerial vehicle 110. The power button310 may toggle the power of the remote controller 120 or toggle thepower of the aerial vehicle 110. In some embodiments, the screen 170 maybe a touch screen and thus can receive user inputs as well.

The remote controller 120 may contain one or more internal directionalantennas (not shown in FIG. 3). For example, the remote controller 120may include two ceramic patch antennas. In some embodiments, thecontroller 120 uses both antennas for transmission and reception. Inalternate embodiments, one antenna is used for reception and the otherfor transmission. The remote controller 120 may also include a Yagi-Udaantenna, a log-periodic antenna, a parabolic antenna, a short backfireantenna, a loop antenna, a helical antenna, a phased array of antennas,any other direction antenna, or some combination thereof.

FIG. 4A illustrates an example embodiment of an electronics and control(EC) system 400 of the aerial vehicle 110. The EC system 400 may includethe flight controller 402, an electronic speed controller 404, one ormore thrust motors 405, a gimbal interface 406, a sensor (or telemetric)subsystem 408, a power subsystem 410, a video link controller 412, acamera interface 414, and a communication subsystem 416. The componentsmay communicate directly or indirectly with each other through a databus on the aerial vehicle 110.

In one embodiment, the communication subsystem 416 may be a long-rangeWi-Fi system. As noted above, the communication subsystem 416 mayinclude or be another wireless communication system, for example, onebased on long term evolution (LTE), 3G, 4G, and/or 5G mobilecommunication standards. The communication subsystem 416 also may beconfigured with a unidirectional RC channel for communication ofcontrols from the remote controller 120 to the aerial vehicle 110 and aseparate unidirectional channel for video downlink from the aerialvehicle 110 to the remote controller 120 (or to a video receiver wheredirect video connection may be desired). The sensor subsystem 408 mayinclude navigational components, for example, a gyroscope,accelerometer, a global positioning system (GPS) and/or a barometricsensor. The telemetric compass may also include an unmanned aerialvehicle (UAV) compass 409. The UAV compass 409 may include one or moremagnetometer sensors with which it determines the orientation of theaerial vehicle 110. The power subsystem 410 may include a battery packand/or a protection circuit module as well as a power control and/orbattery management system. The camera interface 414 may interface withan image capture device or may include an integrated image capturedevice.

The flight controller 402 of the EC system 400 may communicate with theremote controller 120 through the communication subsystem 416. Theflight controller 402 may control the flight related operations of theaerial vehicle 110 by controlling the other components such as theelectronic speed controller 404 and/or the sensor subsystem 408. Theflight controller 402 may control a gimbal 175 through the gimbalinterface 406. The flight controller 402 also may interface with thevideo link controller 412 for operation control of an image capturedevice (e.g., camera 115) coupled to the aerial vehicle 110. The flightcontroller 402 can configure the flight path, the speed, the trajectory,and the position of the aerial vehicle 110 based on input from the user(for instance, via the remote controller 120). In addition, as describedbelow in greater detail, the flight controller 402 can configure theflight path, speed, trajectory, and position of the aerial vehicle 120without receiving input from the user, for instance when the aerialvehicle 120 is adjacent to, within a threshold proximity of, or flyingtowards a virtual wall or NFZ.

The electronic speed controller 404 may be configured to interface withthe thrust motors 405 (via an electronics interface) to control thespeed and thrust applied to the propellers 140 of the aerial vehicle110. The video link controller 412 may be configured to communicate withthe camera interface 414 to capture and transmit images from an imagecapture device to the remote controller 120 (or other device with ascreen such as a smart phone), e.g., via the communication subsystem416. The power subsystem 410 may be configured to manage and supplypower each of the components of the EC system 400.

FIG. 4B illustrates an example interconnect architecture of the aerialvehicle 110 with the gimbal 175. Also shown is a battery 440 as a partof the power subsystem 410 and two antennas 460A-460B as a part of thecommunication subsystem 416. This figure illustrates in an exampleembodiment that the flight controller 402 may be coupled with twoelectronic speed controllers 404. Each electronic speed controller 404in this configuration may drive two thrust motors 405 (via respectivecomponents of each thrust motor).

Also shown is a gimbal interface 406 that may communicatively couple thegimbal controller 420 to components of the EC system 400. In particular,the gimbal interface 406 may be communicatively coupled with the videolink controller 412, the sensor subsystem 408 (e.g., the GPS and/or thecompass), and/or one or more of the antennas 460A-460B. The gimbalinterface 406 may be used to feed data (e.g., telemetric data, controlsignals received from the remote controller 120, and/or video linkcontrol signals) from the video link controller 412, the sensorsubsystem 408, and/or one or more of the antennas 460A-460B to thegimbal controller 420. The gimbal controller 420 may be communicativelycoupled with the camera 115 through one or more camera interfaceconnectors 430. The camera interface connectors 430 may include cameracommunication interfaces such as universal serial bus (USB) and/or HDMI.The media captured by the camera 115 (e.g., still images, video, and/oraudio) may be communicated to the aerial vehicle 110 through the camerainterface connectors 430. Data (e.g., telemetric data from the sensorsubsystem 408) also may be sent via the camera interface connectors 430to the camera 115 to associate with video captured and stored on thecamera 115.

Virtual Walls and No-Fly Zone Navigation

FIG. 5 is a high-level block diagram of the flight controller 402 inaccordance with one embodiment. Some embodiments of the flightcontroller 402 have different components than those described here. Theembodiment of the flight controller 402 illustrated in FIG. 5 includes aNFZ database 501, a user interface 502, a status engine 503, a distanceevaluation engine 504, a navigation engine 505, and a virtual wallbehavior engine 506.

The NFZ database 501 stores information describing NFZ boundaries, suchas a geographic coordinates, locations, and the like. In someembodiments, the NFZ database 501 stores information describing all NFZsin a specified geographic area. For example, the NFZ database 501 maystore coordinates describing NFZs within a specified radius of theaerial vehicle 110. Likewise, the NFZ database 501 may be updated inreal time (e.g., from a server communicatively coupled to the flightcontroller 402) to include additional or different NFZs, for instance asthe aerial vehicle 110 moves to a new location, as time passes, or asenvironmental conditions change. For example, the NFZ information of theNFZ database 501 may be updated as the aerial vehicle 110 travels acrosscounty border lines. As another example, the NFZ database 501 may beupdated to exclude an airport's NFZ information after the last planeshave entered and exited the airport on night. As a further example, theNFZ database 501 may be updated to exclude specific types of NFZs, forinstance as specified by a user via the user interface 502. NFZs may beregistered with a governing entity (e.g., private property orhigh-security NFZs may be registered with local or federal governments),or may be established by rules governing UAV flight (e.g., “stay 1000meters away from airport boundaries). In some embodiments, the NFZdatabase 501 can receive NFZ information from a governing entity withwhich NFZs are registered.

The NFZ database 501 can store many types of NFZ information. Forinstance, NFZs can be defined by specific geographic coordinates, bydata describing dimensions of an NFZ (e.g., a radius of 50 m from aparticular location), or by underlying geographic features or propertylines (e.g., “The White House” or “Mount Rushmore”). In someembodiments, NFZs can vary depending on time, the day, or the season ofthe year. In some embodiments, NFZ data is broken down into datadescribing the individual virtual walls of each NFZ. Additionalembodiments of NFZs not explicitly mentioned here are also possible.Furthermore, any combination of NFZ embodiments is possible.

The user interface 502 receives user input from the remote controller102 requesting movement of the set point of the aerial vehicle 110. Theuser input from remote controller 120 may request a change in the speed,direction, trajectory, or location of the set point of the aerialvehicle 110. Such requests received by the user interface 502 are routedto the navigation engine 505 for implementation. The navigation engine505 is discussed in greater detail below. By changing the parameters ofthe set point of the aerial vehicle 110, the speed, direction,trajectory, and location of the aerial vehicle 110 subsequently changeas the aerial vehicle adjusts its movement in an attempt to reach theset point.

Note that while the processes and steps of NFZ navigation as describedherein focus on the status and adjustment of the set point of the aerialvehicle 110, in some embodiments the same processes and steps of NFZnavigation may be based on the status and adjustment of the aerialvehicle 110 itself, rather than its set point. For example, the userinterface 502 may receive user input from the remote controller 102requesting movement of the aerial vehicle 110, rather than its setpoint. Similarly, the operation of additional components of the flightcontroller 402 may also be based on the status and adjustment of theaerial vehicle 110.

The status engine 503 identifies the state of the set point of theaerial vehicle 110 in real time. Specifically, the status engine 503identifies the current speed, direction, trajectory, and location of theset point in real time.

The distance evaluation engine 504 determines the shortest normaldistances between the set point of the aerial vehicle 110 and one ormore unique virtual walls of a NFZ. Note that in this case, “uniquevirtual walls” refers to virtual walls including at least one differentend point. The distance evaluation engine 504 determines the shortestnormal distances in real time as information describing the location ofthe set point of the aerial vehicle 110 is received from the statusengine 503. One embodiment of the general operation of the distanceevaluation engine 504 is described in further detail with regard to FIG.6.

FIG. 6 is a flow chart of a process for determining distances from theset point of the aerial vehicle 110 to the closest two virtual walls ofa NFZ, in accordance with an embodiment. In alternative embodiments, theprocess for determining distances from the set point of the aerialvehicle 110 to two closest virtual walls can also be performed for a setof multiple NFZs comprising multiple virtual walls.

First, location information describing geographic boundaries of one ormore NFZs is received 610 from the NFZ database 501. The specific NFZsfor which location information is received may be selected in aplurality of ways. In one embodiment, all NFZs stored in the NFZdatabase 501 are selected. In another embodiment, NFZs are selected foranalysis based proximity to the set point of the aerial vehicle 110. Forexample, only NFZs located within a threshold distance of the set pointof the aerial vehicle 110 may be selected. This threshold distance maybe specified within the NFZ database 501, by the distance evaluationengine 504, or by the user of the remote controller 102 via the userinterface 502.

Following receipt of location information describing geographicboundaries of an NFZ 610, a first segment (i.e. a first virtual wall) ofthe NFZ that is closest in proximity to the set point of the aerialvehicle 110 is identified 620. Next, a first distance between the setpoint of the aerial vehicle 110 and the nearest point on the firstsegment (i.e. the first virtual wall) of the NFZ is determined 630. Inother words, steps 620 and 630 determine a first shortest normaldistance between an NFZ and the set point of the aerial vehicle 110.

Steps 620 and 630 are repeated for a second, unique segment (i.e. asecond, unique virtual wall different from the first segment).Specifically, a second NFZ segment (i.e. a second virtual wall) that issecond closest in proximity to the set point of the aerial vehicle 110is identified 640. The second segment identified in step 640 may be anadditional segment of the NFZ from which the first segment wasidentified in step 610, or it may be a segment from an entirelydifferent NFZ. Then, a second distance between the set point of theaerial vehicle 110 and the nearest point on the second NFZ segment (i.e.the second virtual wall) is determined 650. In other words, steps 640and 650 determine a shortest normal distance between a different, secondclosest virtual wall and the set point of the aerial vehicle 110. Itshould be emphasized that in some embodiments, the first distance andthe second distance are determined at substantially the same time orwithin the same processing loop/pass.

While the embodiment of FIG. 6 describes determining two shortest normaldistances between the set point of the aerial vehicle 110 and two uniquevirtual walls of a NFZ, in other embodiments, zero, one, three, or moreshortest normal distances between the set point and NFZ virtual wallsmay be determined. For example, in one embodiment, the set point of theaerial vehicle 110 may be located in a region containing no NFZs (or noNFZs within a threshold distance of the set point). In another example,a NFZ may include only one virtual wall (e.g., a state border), and onlyone shortest normal distance is determined. In some embodiments, the setpoint of the aerial vehicle 110 must be within a threshold distance of avirtual wall for the virtual wall to be considered for the purpose ofdetermining shortest normal distances. In another embodiment, shortestnormal distances are only determined between the set point and virtualwalls that are not obstructed from the set point by other virtual walls(a line can be drawn from the set point to the virtual wall withoutcrossing another virtual wall). In another embodiment, the set point ofthe aerial vehicle 110 may be located such that it is in close proximityto two virtual walls, but positioned such that the point on the NFZ thatis closest in proximity to the set point of the aerial vehicle 110 lieson a vertex connecting the two virtual walls. In such embodiments, theshortest normal distance between the set point and the two virtual wallsis the same. Three embodiments of distance determination by the distanceevaluation engine 504 are illustrated in FIG. 7.

FIG. 7 illustrates three embodiments in which the distance evaluationengine 504 determines up to two shortest normal distances betweendifferent set points of the aerial vehicle 110 and unique virtual wallsof the NFZ 700. The NFZ 700 comprises five unique virtual walls: avirtual wall 710, a virtual wall 720, a virtual wall 730, a virtual wall740, and a virtual wall 750. Note that for illustrative simplicity, FIG.7 assumes that the set point of the aerial vehicle 110 and the aerialvehicle 110 are co-located.

Lines solely comprising dots that connect the aerial vehicle 110 to afirst virtual wall of the NFZ 700 indicate a first shortest normaldistance between the aerial vehicle 110 and the NFZ 700. Linescomprising alternating dots and dashes that connect the aerial vehicle110 to a second, unique virtual wall of the NFZ 700 indicate a shortestnormal distance between the aerial vehicle 110 and a different, secondclosest virtual wall of the NFZ 700.

In a scenario 701, the set point of the aerial vehicle 110 is positionedoutside a convex portion of polygonal the NFZ 700 nearest to the virtualwall 710. Thus the distance evaluation engine 504 only determines asingle closest normal distance 701A between the set point of the aerialvehicle 110 and the virtual wall 710 of the NFZ 700.

A scenario 702 depicts the aerial vehicle 110 as located within aconcave corner of the polygonal the NFZ 700 between the virtual wall 720and the virtual wall 730. Two shortest normal distances from the setpoint of the aerial vehicle 110 to the unique virtual walls of the NFZ700 are determined by the distance evaluation engine 504. Note that theclosest the virtual wall 730 and the second closest the virtual wall 720of the NFZ 700 are unique walls. Specifically, the closest the virtualwall 730 and the second closest the virtual wall 720 of the NFZ 700share at least one different endpoint. The shortest normal distance fromthe set point of the aerial vehicle 110 to the virtual wall 730 isdenoted by 702A. The second shortest normal distance from the set pointof the aerial vehicle 110 to the virtual wall 720 is denoted by 702B.

A scenario 703 depicts the aerial vehicle 110 as positioned outside aconvex portion of polygonal the NFZ 700. The aerial vehicle 110 ispositioned such that the nearest point on the two closest virtual walls740 and 750 is the same point. Specifically, the nearest point on bothof the two virtual walls 740 and 750 is the vertex connecting the twovirtual walls 740 and 750. As a single closest distance applies to bothvirtual walls, only one distance 703A is determined by the distanceevaluation engine 504.

Turning back to FIG. 5, the navigation engine 505 instructs the movementof the set point of the aerial vehicle 110 based on user input receivedvia the user interface 502 and instructions received from the virtualwall behavior engine 506. The virtual wall behavior engine 506 isdescribed below in further detail. Specifically, the navigation engine505 may change the speed, direction, trajectory, or location of the setpoint of the aerial vehicle 110. By changing the parameters of the setpoint of the aerial vehicle 110, the speed, direction, trajectory, andlocation of the aerial vehicle 110 subsequently change. Note that theremay be lag time between instruction of the set point movement by thenavigation engine 505 and adherence of the aerial vehicle 110 to theinstruction.

Commands received by the navigation engine 505 from the virtual wallbehavior engine 506 override user input received via the user interface502. In other words, when faced with conflicting commands from the userinterface 502 and the virtual wall behavior engine 506, the navigationengine 505 moves the set point of the aerial vehicle 110 according tothe instructions of the virtual wall behavior engine 505. Wheninstructions are not received from the virtual wall behavior engine 506,or when instructions received from the user interface 502 comply withthe restrictions received from the virtual wall behavior engine 506, thenavigation engine 505 moves the set point of the aerial vehicle 110according to commands from the user interface 502.

The virtual wall behavior engine 506 establishes restrictions on themovement of the set point of the aerial vehicle 110 based on informationfrom the status engine 503 and the distance evaluation engine 504 toensure that the aerial vehicle 110 does not fly into NFZs. Specifically,the virtual wall behavior engine 506 sends restrictions on the speed,direction, and trajectory of the set point of the aerial vehicle 110 tothe navigation engine 505 in real time. By restricting the parameters ofthe set point of the aerial vehicle 110, the speed, direction,trajectory, and location of the aerial vehicle 110 are subsequentlyrestricted. One embodiment of the general operation of the virtual wallbehavior engine 506 is described in further detail with regard to FIG.8.

FIG. 8 a flow chart of a process for modifying the movement of the setpoint of the aerial vehicle 110, in accordance with an embodiment. Inthe embodiment of FIG. 8, a geographic location of the set point of theaerial vehicle 110 is determined 810 using input from the status engine503. Next, the NFZ database 501 is queried to determine 820 a geographiclocation of a virtual wall. The specific virtual wall chosen foranalysis in step 820 may be selected in a plurality of ways. Forinstance, the virtual wall may be chosen based on its inclusion in aspecific NFZ, based on proximity of the virtual wall to the aerialvehicle 110 or the set point (e.g., the closest virtual wall to the setpoint), based on user input, or based on any other suitable criteria.

After the geographic location of the virtual wall is determined 820, thedistance evaluation engine 504 determines 830 a distance between the setpoint of the aerial vehicle 110 and the nearest point on the virtualwall (the “shortest normal distance”). Next, the distance evaluationengine 504 determines 840 whether the shortest normal distance is lessthan a threshold distance. This threshold distance may be specifiedwithin the NFZ database 501, by the virtual wall behavior engine 506, orby the user of the remote controller 102 via the user interface 502. Insome embodiments, the threshold distance is referred to as a“deceleration zone” of the working virtual wall.

Finally, dependent upon the location of the set point of the aerialvehicle 110 relative to the deceleration zone, the virtual wall behaviorengine 506 modifies 850 one or more of the velocity of the set point ofthe aerial vehicle 110 and the trajectory of the set point of the aerialvehicle 110 such that the aerial vehicle 110 does not cross the virtualwall. This modification is then relayed to the navigation engine 505 asdescribed previously. Several embodiments of step 850 are discussed withregard to FIGS. 9A, 9B, and 9C.

FIG. 8 describes one embodiment of the general operation of the virtualwall behavior engine 506. However, additional nuanced embodiments of theoperation of the virtual wall behavior engine 506 are availabledepending on the mode of operation under which the virtual wall behaviorengine 506 operates. Three example modes of operation available to thevirtual wall behavior engine 506 include: a free-sliding mode ofoperation, a restricted-sliding mode of operation, and a no-sliding modeof operation. Each mode of operation provides a different set ofbehavior nuances to the operation of the virtual wall behavior engine506. These modes of operation are meant to enable smoother navigation ofthe aerial vehicle 110 around virtual walls of an NFZ. The three modesof operation listed above are described in further detail with regard toFIGS. 9A, 9B, and 9C respectively.

The mode of operation of the virtual wall behavior engine 506 may beselected by the programmer of controller 402 (e.g., a default mode ofoperation setting), by user input to the user interface 502, or by anyother suitable means. In one embodiment, the working mode of operationof the virtual wall behavior engine 506 is fixed. In an alternativeembodiment, the working mode of operation of the virtual wall behaviorengine 506 may be configured in real time. In various embodiments, eachNFZ stored in the NFZ database 501 may be associated with a specificmode of operation of the virtual wall behavior engine 506. For example,when the set point of the aerial vehicle 110 comes within a specifieddistance of an NFZ associated with the restricted-sliding mode ofoperation, the virtual wall behavior engine 506 may automatically beconfigured to operate in the restricted-sliding mode of operation. Infurther embodiments, the working mode of operation of the virtual wallbehavior engine 506 may be configured based on the location of the setpoint of the aerial vehicle 110 relative to a NFZ. For example, when theset point of the aerial vehicle 110 is determined to be located within aconcave corner of a NFZ, the virtual wall behavior engine 506 mayautomatically be configured to operate in the restricted-sliding mode ofoperation. Additional embodiments not explicitly mentioned here are alsopossible. Furthermore, any combination of these embodiments is possible.

Each mode of operation defines a unique set of behavioral parametersapplied by the aerial vehicle 110 as the aerial vehicle encounters anNFZ when operating in that mode of operation. These NFZ parameters areused by the virtual wall behavior engine 506 in instructing the movementof the set point of the aerial vehicle 110 under the mode of operation.Thus prior to describing each mode of operation, the set of NFZparameters corresponding to the mode of operation will be described.

FIG. 9A illustrates the aerial vehicle 110 navigating the areasurrounding a NFZ 900A when operating in the free-sliding mode ofoperation. Note that the free-sliding mode of operation described hereinmay apply to the operation of the aerial vehicle 110 in any alternativeenvironment containing any alternative NFZ. For example, the aerialvehicle 110 may be located outside of a convex corner of an NFZ ratherthan within a concave corner as shown in FIG. 9A.

Under the free-sliding mode of operation, each virtual wall of each NFZhas a corresponding zone of deceleration. A zone of deceleration is aboundary area that extends a specified distance from a virtual wall of aNFZ in the direction opposite the interior of the NFZ. The width ofextension of the zone of deceleration is uniform along the entire lengthof a virtual wall. Two examples of zones of deceleration can be seen inFIG. 9A. The zone of deceleration of a virtual wall 901 is indicated bythe cross-hatched area. The zone of deceleration of a virtual wall 902is indicated by the dotted area. Note that two or more zones ofdeceleration may overlay one another as shown in FIG. 9A.

Each point along the width of a zone of deceleration is associated witha velocity scaling factor. Velocity scaling factors are used toconstrain the velocity of the set point of the aerial vehicle 110 as itapproaches a virtual wall under the free-sliding mode of operation. Asshown in FIG. 9A, f₁ is the velocity scaling factor associated with thepoint along the width of the zone of deceleration of the virtual wall901 that is furthest from the virtual wall 901. f₂ is the velocityscaling factor associated with the point along the width of the zone ofdeceleration of the virtual wall 901 that is co-located on the virtualwall 901. Each point along the width of the zone of deceleration of thevirtual wall 901 that is between the outermost point of the zone ofdeceleration of the virtual wall 901 and the innermost point of the zoneof deceleration of the virtual wall 901 is also associated with avelocity scaling factor. Thus the width of the zone of deceleration ofthe virtual wall 901 is associated with an array of velocity scalingfactors. A similar pattern applies to the zone of deceleration of thevirtual wall 902.

An array of velocity scaling factors corresponding to a zone ofdeceleration may follow a specified distribution. For example, in FIG. 9the velocity scaling factors within the array corresponding to the zoneof deceleration of the virtual wall 901 decrease linearly from f₁ to f₂,where f₁ is equal to 1 and f₂ is equal to 0. The same linear decreasingdistribution applies to the array of velocity scaling factors f₃ to f₄that corresponds to the zone of deceleration of the virtual wall 902.Note that while the zones of deceleration depicted in FIG. 9A areassociated with a linear array of velocity scaling factors withendpoints f₁ and f₂ equal to 1 and 0 respectively, a zone ofdeceleration may be described by any set of scaling factors, any scalingdistribution, and any endpoints of the zone of deceleration.

The starting position of the set point of the aerial vehicle 110 isindicated by the UAV icon in FIG. 9A. From its starting position, theset point of the aerial vehicle 110 travels at a velocity v_(initial)along the trajectory indicated by the corresponding arrow. For theexample shown in FIG. 9A, it is assumed that v_(initial) is the maximumoverall possible speed of the aerial vehicle 110. The components of thevelocity v_(initial) that are perpendicular and parallel to the virtualwall 901 are v_(f) and v_(s) respectively. Specifically, v_(f) is thecomponent of the initial velocity of the set point of the aerial vehicle110 that is perpendicular to the nearest virtual wall of the NFZ 900A.This nearest virtual wall is the virtual wall 901 in FIG. 9A. V_(s) isthe component of the initial velocity of the set point of the aerialvehicle 110 that is perpendicular to the second nearest virtual wall ofthe NFZ 900A. This second nearest virtual wall is the virtual wall 902in FIG. 9A.

When the set point of the aerial vehicle 110 enters the zone ofdeceleration of the virtual wall 901 as depicted in step 2 of FIG. 9A,the velocity of the set point of the aerial vehicle 110 is partiallyrestricted based on the set point's distance from the virtual wall 901.Specifically, the component of the velocity that is parallel to thevirtual wall 901 remains the same, but the component of the velocityperpendicular to the virtual wall 901 adheres to a maximum velocity thatis determined by multiplying the maximum possible velocity of the aerialvehicle 110 by the velocity scaling factor associated with the pointalong the width of the zone of deceleration at which the set point islocated. Because the array of velocity scaling factors of the zone ofdeceleration of the virtual wall 901 linearly decreases from 1 to 0 fromthe outer edge of the zone of deceleration to the inner edge of the zoneof deceleration, the component of the velocity perpendicular to thevirtual wall 901 decreases linearly as the set point approaches thevirtual wall 901. For example, if the overall maximum velocity of theaerial vehicle 110 is 15 m/s and the set point of the aerial vehicle 110is located at the midpoint of the width of the zone of decelerationwhere the velocity scaling factor is equal to 0.5, the component of thevelocity perpendicular to the virtual wall 901 is restricted to 7.5 m/s.Because the component of the velocity perpendicular to the virtual wall901 is linearly restricted according to its location but the componentof the velocity parallel to the virtual wall 901 stays the same, thetrajectory of the set point of the aerial vehicle 110 is asymptotic asit approaches the virtual wall 901.

Finally, when the set point of the aerial vehicle 110 reaches the edgeof the zone of deceleration that is co-located with the virtual wall901, the velocity scaling factor f₂ is equal to 0 and thus the componentof the velocity perpendicular to the virtual wall 901 also becomes zero.As a result, the aerial vehicle 110 simply travels parallel to thevirtual wall 901 towards the virtual wall 902 at velocity v_(s).

Note that the component of the velocity of the set point of the aerialvehicle 110 that is perpendicular to the virtual wall in question cannotexceed the maximum velocity determined by the relevant velocity scalingfactor. However the velocity of the set point of the aerial vehicle 110that is perpendicular to the virtual wall in question can be less thanthe maximum velocity. For example, if the set point of the aerialvehicle 110 moves at a constant velocity of 7.5 m/s in a directionperpendicular to the virtual wall 901 under the conditions outlinedabove, its velocity will not change until it passes the midpoint of thezone of deceleration of the virtual wall 901 where the velocity isrestricted to a maximum of 7.5 m/s. In some embodiments, when the setpoint of the aerial vehicle moves at a rate slower than the restrictedmaximum rate of 7.5 m/s, the velocity of the set point will not changeuntil the set passes some threshold distance after the midpoint of thezone of deceleration corresponding to the velocity of the set point.

Turning back to FIG. 9A, as shown in step 3, when the set point of theaerial vehicle 110 enters the zone of deceleration of the virtual wall902, the velocity of the set point of the aerial vehicle 110 is furtherrestricted, this time based on the set point's distance from the virtualwall 902. As in the case in which the set point of the aerial vehicle110 approached the virtual wall 901, the component of the velocity ofthe set point of the aerial vehicle 110 that is parallel to the virtualwall 902 remains the same, but the component of the velocity of the setpoint of the aerial vehicle 110 that is perpendicular to the virtualwall 902 adheres to a maximum velocity calculated by multiplying themaximum possible velocity of the aerial vehicle 110 by the velocityscaling factor associated with the point along the width of the zone ofdeceleration at which the set point of the aerial vehicle 110 islocated. Recall from the description of step 2 that the component of thevelocity of the set point of the aerial vehicle 110 that is parallel tothe virtual wall 902 is equal to 0 and the component of the velocity ofthe set point of the aerial vehicle 110 that is perpendicular to thevirtual wall 902 is v_(s).

As described previously, the array of velocity scaling factorscorresponding the width of the zone of deceleration of the virtual wall902 is similar to that of the zone of deceleration of the virtual wall901. Specifically, the velocity scaling factor f₃ is equal to 1, thevelocity scaling factor f₄ is equal to 0, and a linear, decreasingdistribution of velocity scaling factors exists in between f₃ and f₄.Thus as the set point of the aerial vehicle 110 approaches the virtualwall 902, the component of the velocity parallel to the virtual wall 902remains the same at a value of zero, but the component of the velocityof the set point of the aerial vehicle 110 that is perpendicular to thevirtual wall 902 decreases linearly until it becomes zero when the setpoint reaches the edge of the zone of deceleration of the virtual wall902. Then the aerial vehicle 110 hovers with an overall velocity equalto zero at the vertex between virtual walls 901 and 902 until thelocation of the set point is changed.

In order to leave the corner created by the vertex of virtual walls 901and 902, the location of the set point of the aerial vehicle 110 must bechanged such that at least one component of the velocity of the setpoint of the aerial vehicle 110 is at least partially directed in theopposite direction of at least one of the virtual walls 901 and 902. Anycomponent of the velocity of the set point the aerial vehicle 110 thatis opposite the direction of at least one virtual wall in the embodimentof FIG. 9a is not restricted. In general, when the set point the aerialvehicle 110 moves out of a zone of deceleration and away from a virtualwall, its velocity is not restricted under the free-sliding mode ofoperation. This results in smooth motion, with no jumps in velocity, ofthe aerial vehicle 110 as it leaves a zone of deceleration.

The purpose of the embodiment of the free-sliding mode of operationillustrated in FIG. 9A is to demonstrate the principles of thefree-sliding mode of operation. These same principles demonstrated withregard to the FIG. 9A embodiment can also be applied to any alternativeNFZ encountered by the aerial vehicle 110 when operating in thefree-sliding mode of operation.

FIG. 9B illustrates the aerial vehicle 110 navigating the areasurrounding a NFZ 900B when operating in the restricted-sliding mode ofoperation. Note that the restricted-sliding mode of operation describedherein may apply to the operation of the aerial vehicle 110 in anyalternative environment containing any alternative NFZ. For example, theaerial vehicle 110 may be within a concave corner of an NFZ rather thanoutside of a convex area as shown in FIG. 9B.

Under the restricted-sliding mode of operation, each virtual wall ofeach NFZ has a corresponding zone of deceleration. Like the zones ofdeceleration described with regard to FIG. 9A, a zone of decelerationunder the restricted-sliding mode of operation is a boundary area thatextends a specified distance from a virtual wall of a NFZ in thedirection opposite the interior of the NFZ. Also similarly, the width ofextension of the zone of deceleration is uniform along the entire lengthof a virtual wall.

One example of a zone of deceleration used by the restricted-slidingmode of operation can be seen in FIG. 9B with regard to a virtual wall903. One noticeable discrepancy between the zones of decelerationassociated with the free-sliding mode of operation and the zones ofdeceleration associated with the restricted-sliding mode of operation isthe separation of the zones of deceleration of the restricted-slidingmode of operation into two distinct sections as seen in FIG. 9B. Thisdistinction is discussed in further detail below.

As under the free-sliding mode of operation, under therestricted-sliding mode of operation each point along the width of azone of deceleration is associated with a velocity scaling factor.Velocity scaling factors are used to constrain the velocity of the setpoint of the aerial vehicle 110 as it both approaches and escapes avirtual wall under the restricted-sliding mode of operation. As shown inFIG. 9B, f₁ is the velocity scaling factor associated with the pointalong the width of the zone of deceleration of the virtual wall 903 thatis furthest from the virtual wall 903. f₂ is the velocity scaling factorassociated with the point along the width of the zone of deceleration ofthe virtual wall 903 that is co-located on the virtual wall 903. Eachpoint along the width of the zone of deceleration of the virtual wall903 that is between the outermost point of the zone of deceleration ofthe virtual wall 903 and the innermost point of the zone of decelerationof the virtual wall 903 is also associated with a velocity scalingfactor. Thus the width of the zone of deceleration of the virtual wall903 is associated with an array of velocity scaling factors.

Also like the free-sliding mode of operation, under therestricted-sliding mode of operation an array of velocity scalingfactors corresponding to a zone of deceleration may follow a specifieddistribution. For example, in FIG. 9B the velocity scaling factorswithin the array corresponding to the zone of deceleration of thevirtual wall 903 decrease linearly from f₁ to f₂, where f₁ is equal to 1and f₂ is equal to 0. Note that while the zone of deceleration depictedin FIG. 9B is associated with a linear array of velocity scaling factorswith endpoints f₁ and f₂ equal to 1 and 0 respectively, a zone ofdeceleration under the restricted-sliding mode of operation may bedescribed by any set of scaling factors, any scaling distribution, andany endpoints of the zone of deceleration.

As depicted in FIG. 9B, zones of deceleration under therestricted-sliding mode of operation are partitioned into two sectionsat a point along the width of the zone of deceleration. For addedclarity, FIG. 9B depicts the two separated sections of the zone ofdeceleration of the virtual wall 903 using two different patterns. Thesection of the zone of deceleration of the virtual wall 903 denoted bythe striped pattern will hereafter be referred to as the “distalsection” of the zone of deceleration. The section of the zone ofdeceleration of the virtual wall 903 denoted by the cross-hatchedpattern will hereafter be referred to as the “proximal section” of thezone of deceleration. Note that the zone of declaration of the virtualwall 903 encompasses both the distal and the proximal sections. The twoseparate sections of the zones of deceleration established under therestricted-sliding mode of operation restrict the movement of the setpoint of the aerial vehicle 110 in different ways. The details of thesedifferential restrictions are explored in depth below.

The point at which the separation of the zone of deceleration occurs ishereafter referred to as the “switch point” of the zone of deceleration.Like all other points along the width of a zone of deceleration, theswitch point is associated with a velocity scaling factor ‘f_(switch)’as shown in FIG. 9B. Because f_(switch) is included within the array ofvelocity scaling factors associated with the width of a zone ofdeceleration, the value of f_(switch) varies depending on where theswitch point is located along the width of a zone of deceleration. Inthe embodiment depicted in FIG. 9B, the switch point is located exactlyat the midpoint of the width of the zone of deceleration of the virtualwall 903. Because the array of velocity scaling factors associated withthe width of that zone of deceleration of the virtual wall 903 follows alinear decreasing distribution from 1 to 0, it follows that the value off_(switch) is equal to 0.5.

The location of the switch point, and thus the value of f_(switch), maybe specified within the NFZ database 501, by the virtual wall behaviorengine 506, or by the user of the remote controller 102 via the userinterface 502. In alternative embodiments, the array of velocity scalingfactors associated with the width of a zone of deceleration may adhereto any distribution and the switch point may be located at any pointalong the width of a zone of deceleration. Thus the value f_(switch) mayvary based on the location within the zone of deceleration correspondingto the switch point, and/or based on the distribution of scaling factorswithin the zone of deceleration.

The starting position of the set point of the aerial vehicle 110 isindicated by the UAV in FIG. 9B. From its starting position, the setpoint of the aerial vehicle 110 travels at a velocity v_(initial) alongthe trajectory indicated by the corresponding arrow. For the exampleshown in FIG. 9B, it is assumed that v_(initial) is the maximum overallpossible speed of the aerial vehicle 110. v_(f) is the component of theinitial velocity of the set point of the aerial vehicle 110 that isperpendicular to the nearest virtual wall of the NFZ 900B. This nearestvirtual wall is the virtual wall 903 in FIG. 9B. Note that there is nosecond closest virtual wall in the embodiment depicted in FIG. 9B.

When the set point of the aerial vehicle 110 enters the distal sectionof the zone of deceleration of the virtual wall 903 as depicted in step2 of FIG. 9B, the velocity of the set point of the aerial vehicle 110 isrestricted based on the set point's distance from the virtual wall 903.However unlike under the free-sliding mode of operation, under therestricted-sliding mode of operation, the entire magnitude of thevelocity of the set point of the aerial vehicle 110 is restricted—notjust a single component. Specifically, the overall velocity of theaerial vehicle 110 adheres to a maximum velocity that is determined bymultiplying the maximum possible velocity of the aerial vehicle 110 bythe velocity scaling factor associated with the point along the width ofthe zone of deceleration at which the set point is located. Because thearray of velocity scaling factors of the zone of deceleration of thevirtual wall 903 linearly decreases from 1 to 0 from the outer edge ofthe zone of deceleration to the inner edge of the zone of deceleration,the overall velocity of the set point of the aerial vehicle 110decreases linearly as the set point approaches the proximal section ofthe zone of deceleration of the virtual wall 903. For example, if theoverall maximum velocity of the aerial vehicle 110 is 15 m/s and the setpoint of the aerial vehicle 110 is located at the midpoint of the distalsection of the zone of deceleration where the velocity scaling factor isequal to 0.75, the overall velocity of the set point is restricted to11.25 m/s. Because all components of the velocity are linearlyrestricted by the same factor, the trajectory of the set point of theaerial vehicle 110 is linear as it approaches the switch point and theproximal section of the zone of deceleration of the virtual wall 903. Inother words, the magnitude of the velocity of the set point of theaerial vehicle 110 decreases, but the direction of the velocity remainsconstant.

As soon as the set point of the aerial vehicle 110 crosses the switchpoint the zone of deceleration of the virtual wall 903 and enters theproximal section of the zone of deceleration of the virtual wall 903 asdepicted in step 3 of FIG. 9B, the component of the velocity of the setpoint of the aerial vehicle 110 that is perpendicular to the virtualwall 903 is restricted as described in the free-sliding mode ofoperation. However, unlike under the free-sliding mode of operation, thecomponent of the velocity of the set point of the aerial vehicle 110that is parallel to the virtual wall 903 also continues to be restrictedbased on the restriction of the parallel component when the set point islocated within the distal section of the zone of deceleration, though isnot restricted further.

Specifically, the component of the velocity perpendicular to the virtualwall 903 adheres to a maximum velocity that is determined by multiplyingthe maximum possible velocity of the aerial vehicle 110 by the velocityscaling factor associated with the point along the width of the zone ofdeceleration at which the set point is located. Because the array ofvelocity scaling factors of the zone of deceleration of the virtual wall903 linearly decreases from 1 to 0 from the outer edge of the zone ofdeceleration to the inner edge of the zone of deceleration, thecomponent of the velocity perpendicular to the virtual wall 903decreases linearly as the set point approaches the virtual wall 903. Forexample, if the overall maximum velocity of the aerial vehicle 110 is 15m/s and the set point of the aerial vehicle 110 is located at themidpoint of the proximal section of the zone of deceleration where thevelocity scaling factor is equal to 0.25, the component of the velocityperpendicular to the virtual wall 903 is restricted to 3.75 m/s.

Additionally, the component of the velocity that is parallel to thevirtual wall 903 adheres to a constant maximum velocity that isdetermined by multiplying the maximum possible velocity of the aerialvehicle 110 by the velocity scaling factor of the switch point,f_(switch). This restriction on the parallel component of the velocityof the set point of the aerial vehicle 110 remains constant throughoutthe entire proximal section of the zone of deceleration of the virtualwall 903. For example, if the overall maximum velocity of the aerialvehicle 110 is 15 m/s and the switch point of the aerial vehicle 110 islocated at the midpoint of the zone of deceleration where f_(switch) isequal to 0.5, the component of the velocity parallel to the virtual wall903 is restricted to 7.5 m/s at any point within the proximal section ofthe zone of deceleration of the virtual wall 903. Because the componentof the velocity perpendicular to the virtual wall 903 is linearlyrestricted according to its location but the component of the velocityparallel to the virtual wall 903 is restricted at a constant value, thetrajectory of the set point of the aerial vehicle 110 within theproximal section of the zone of deceleration is asymptotic as itapproaches the virtual wall 903.

Finally, when the set point of the aerial vehicle 110 reaches the edgeof the zone of deceleration that is co-located with the virtual wall903, the velocity scaling factor f₂ is equal to 0 and thus the componentof the velocity perpendicular to the virtual wall 903 also becomes zero.As a result, the aerial vehicle 110 simply travels parallel to thevirtual wall 903 at a velocity that remains restricted in the mannerdescribed above. Because there is no second closest virtual wall in theembodiment depicted in FIG. 9B, the aerial vehicle 110 does not getstuck in a convex NFZ corner as in FIG. 9A. Instead, the aerial vehicle110 is able to continue traveling parallel to the virtual wall 903.However using the same principle outlined above, the restricted-slidingmode of operation is able to function in any alternative environment,including one in which a corner similar to the one depicted in FIG. 9Ais present.

Note that the velocity of the set point of the aerial vehicle 110 inboth the distal and proximal sections of the zone of deceleration of thevirtual wall 903 cannot exceed the maximum velocity determined by therelevant velocity scaling factor. However the velocity component(s) ofthe set point of the aerial vehicle 110 can be less than the maximumvelocity. For example, if set point of the aerial vehicle 110 moves at aconstant velocity of 3.75 m/s in the direction perpendicular to thevirtual wall 903 under the conditions outlined above, its velocity willnot change until it passes the midpoint of the proximal section of thezone of deceleration of the virtual wall 903 where the velocity isrestricted to a maximum of 3.75 m/s.

In order to leave the zone of deceleration of the virtual wall 903, thelocation of the set point of the aerial vehicle 110 must be changed suchthat at least one component of the velocity of the set point of theaerial vehicle 110 is at least partially directed in the oppositedirection of the virtual wall 903. In some embodiments, under therestricted-sliding mode of operation, any component of the escapevelocity of the set point of the aerial vehicle 110 that isperpendicular to the virtual wall 903 is not restricted. However, anycomponent of escape velocity of the set point of the aerial vehicle 110that is parallel to the virtual wall 903 is restricted to follow aparabolic trajectory (where the scaling of the parallel velocitycomponent decreases with an increase in distance from the virtual wall).

In some embodiments, under the restricted-sliding mode of operation,when leaving the zone of deceleration, the overall magnitude of thevelocity of the set point is constrained to a maximum velocity (V_(E)).V_(E) can be dependent on the trajectory of the set point and thedistance of the set point to the virtual wall 903. In some embodiments,V_(E) can be computed by superimposing an ellipse over the set pointsuch that a length of the semi-minor axis of the ellipse is selectedbased on the distance of the set point to the virtual wall, and suchthat the semi-major axis of the ellipse is set to 1. V_(E) can then becomputed based on the distance from the center of the ellipse to thelocation on the ellipse boundary where the trajectory vector of the setpoint crosses the ellipse boundary. For instance, if the trajectory ofthe set point is exactly perpendicular to the virtual wall and to theoutside of the deceleration zone, then V_(E) is not constrained at all.Similarly, if the trajectory of the set point is parallel to the virtualwall, V_(E) will be constrained to 0 if the set point is located at thevirtual wall, will be constrained to 50% of the maximum set pointvelocity if the set point is located in the middle of the decelerationzone, and will be constrained to the maximum set point velocity if theset point is located on the outer border of the deceleration zone.Finally, if the trajectory of the set point is between parallel to thevirtual wall and perpendicular to the virtual wall, the V_(E) isconstrained based on the distance of the set point to the intersectionof the boundary of the ellipse and the trajectory vector of the setpoint. Constraining exit velocity as described in this embodimentbeneficially reduces or eliminates discontinuities in velocity as theset point navigates towards and then away from a virtual wall. It shouldbe noted that in some embodiments, the exit velocity of the set pointcan be constrained in other ways, for instance such that the overallmagnitude of the set point velocity is constrained, such that only thecomponent of the set point velocity parallel to the virtual wall isconstrained, based on the trajectory of the set point relative to thevirtual wall, based on the distance of the set point to the virtual wallor within the deceleration zone, or based on any other suitable factor.

The purpose of the embodiment of the restricted-sliding mode ofoperation illustrated in FIG. 9B is to demonstrate the principles of therestricted-sliding mode of operation. These same principles demonstratedwith regard to the FIG. 9B embodiment can also be applied to anyalternative NFZ encountered by the aerial vehicle 110 when operating inthe restricted-sliding mode of operation.

FIG. 9C illustrates the aerial vehicle 110 navigating the areasurrounding a NFZ 900C when operating in the non-sliding mode ofoperation. Note that the restricted-sliding mode of operation describedherein may apply to the operation of the aerial vehicle 110 in anyalternative environment containing any alternative NFZ. For example, theaerial vehicle 110 may be within a concave corner of an NFZ rather thanoutside of a convex area as shown in FIG. 9C.

Under the non-sliding mode of operation, each virtual wall of each NFZhas a corresponding zone of deceleration. Like the zones of decelerationdescribed with regard to FIGS. 9A and 9B, a zone of deceleration underthe non-sliding mode of operation is a boundary area that extends aspecified distance from a virtual wall of a NFZ in the directionopposite the interior of the NFZ. Also similarly, the width of extensionof the zone of deceleration is uniform along the entire length of avirtual wall. One example of a zone of deceleration used by thenon-sliding mode of operation can be seen in FIG. 9C. The zone ofdeceleration of a virtual wall 904 is indicated by the cross-hatchedarea.

Each point along the width of a zone of deceleration is associated witha velocity scaling factor. Velocity scaling factors are used toconstrain the set point of velocity of the aerial vehicle 110 as it bothapproaches and escapes a virtual wall under the non-sliding mode ofoperation. As shown in FIG. 9C, f₁ is the velocity scaling factorassociated with the point along the width of the zone of deceleration ofthe virtual wall 904 that is furthest from the virtual wall 904. f₂ isthe velocity scaling factor associated with the point along the width ofthe zone of deceleration of the virtual wall 904 that is co-located onthe virtual wall 904. Each point along the width of the zone ofdeceleration of the virtual wall 904 that is between the outermost pointof the zone of deceleration of the virtual wall 904 and the innermostpoint of the zone of deceleration of the virtual wall 904 is alsoassociated with a velocity scaling factor. Thus the width of the zone ofdeceleration of the virtual wall 904 is associated with an array ofvelocity scaling factors.

An array of velocity scaling factors corresponding to a zone ofdeceleration of the non-sliding mode of operation may follow a specifieddistribution. In FIG. 9C the velocity scaling factors within the arraycorresponding to the zone of deceleration of the virtual wall 904decrease linearly from f₁ to f₂, where f₁ is equal to 1 and f₂ is equalto 0. Note that while the zone of deceleration depicted in FIG. 9C isassociated with a linear array of velocity scaling factors withendpoints f₁ and f₂ equal to 1 and 0 respectively, a zone ofdeceleration may be described by any set of scaling factors, any scalingdistribution, and any endpoints of the zone of deceleration.

FIG. 9C depicts the zone of deceleration of the virtual wall 904 aspartitioned into two sections by a dashed line beginning at a pointalong the width of the zone of deceleration of the virtual wall 904. Asunder the restricted-sliding mode of operation depicted in FIG. 9B, thepoint at which this separation of the zone of deceleration occurs is the“switch point” of the zone of deceleration. Like all other points alongthe width of a zone of deceleration, the switch point is associated witha velocity scaling factor ‘f_(switch)’ as shown in FIG. 9C. Becausef_(switch) is a member of the array of velocity scaling factorsassociated with the width of a zone of deceleration, the value off_(switch) varies depending on where the switch point is located alongthe width of a zone of deceleration. In the embodiment depicted in FIG.9C, the switch point is located exactly at the midpoint of the width ofthe zone of deceleration of the virtual wall 904. Because the array ofvelocity scaling factors associated with the width of that zone ofdeceleration of the virtual wall 904 follows a linear decreasingdistribution from 1 to 0, it follows that the value of f_(switch) isequal to 0.5.

The location of the switch point, and thus the value of f_(switch), maybe specified within the NFZ database 501, by the virtual wall behaviorengine 506, or by the user of the remote controller 102 via the userinterface 502. In alternative embodiments, the array of velocity scalingfactors associated with the width of a zone of deceleration may adhereto any distribution and the switch point may be located at any pointalong the width of a zone of deceleration. Thus the value f_(switch) mayvary.

Unlike under the restricted-sliding mode of operation, under thenon-sliding mode of operation, the partitioning of a zone ofdeceleration does not affect the velocity of the set point of the aerialvehicle 110 as it approaches a virtual wall. Rather, the partitioning ofthe zone of deceleration restricts the velocity of the set point of theaerial vehicle 110 as it leaves the zone of deceleration. This impact onthe escape velocity of the set point of the aerial vehicle 110 isdescribed in further detail below.

The starting position of the set point of the aerial vehicle 110 isindicated by the UAV icon in FIG. 9C. From its starting position, theset point of the aerial vehicle 110 travels at a velocity v_(initial)along the trajectory indicated by the corresponding arrow. For theexample shown in FIG. 9C, it is assumed that v_(initial) is the maximumoverall possible speed of the aerial vehicle 110. v_(f) is the componentof the initial velocity of the set point of the aerial vehicle 110 thatis perpendicular to the nearest virtual wall of the NFZ 900C. Thisnearest virtual wall is the virtual wall 904 in FIG. 9C. Note that thereis no second closest virtual wall in the embodiment depicted in FIG. 9C.

When the set point of the aerial vehicle 110 enters the zone ofdeceleration of the virtual wall 904 as depicted in step 2 of FIG. 9C,the velocity of the set point of the aerial vehicle 110 is restrictedbased on the set point's distance from the virtual wall 904.Specifically, the overall velocity of the aerial vehicle 110 adheres toa maximum velocity that is determined by multiplying the maximumpossible velocity of the aerial vehicle 110 by the velocity scalingfactor associated with the point along the width of the zone ofdeceleration at which the set point is located. Because the array ofvelocity scaling factors of the zone of deceleration of the virtual wall904 linearly decreases from 1 to 0 from the outer edge of the zone ofdeceleration to the inner edge of the zone of deceleration, the overallvelocity of the set point of the aerial vehicle 110 decreases linearlyas the set point approaches the virtual wall 904. For example, if theoverall maximum velocity of the aerial vehicle 110 is 15 m/s and the setpoint of the aerial vehicle 110 is located at the midpoint of the zoneof deceleration where the velocity scaling factor is equal to 0.5, theoverall velocity is restricted to 7.5 m/s. Because all components of thevelocity are linearly restricted by the same factor, the trajectory ofthe set point of the aerial vehicle 110 is linear as it approaches thevirtual wall 904. In other words, the magnitude of the velocity of theset point of the aerial vehicle 110 decreases, but the direction of thevelocity remains constant.

Finally, when the set point of the aerial vehicle 110 reaches the edgeof the zone of deceleration that is co-located with the virtual wall904, the velocity scaling factor f₂ is equal to 0 and thus the overallvelocity of the set point of aerial vehicle also becomes zero. As aresult, the aerial vehicle 110 simply hovers at the point along thevirtual wall 904 where it came to a stop until the location of its setpoint is changed. In other words, no sliding along the virtual wall 904occurs. This final step is depicted as step 3 of FIG. 9C.

In order to leave the zone of deceleration of the virtual wall 904, thelocation of the set point of the aerial vehicle 110 must be changed suchthat at least one component of the velocity of the set point of theaerial vehicle 110 is at least partially directed in the oppositedirection of the virtual wall 904. Under the non-sliding mode ofoperation, when the set point is located between f₂ and f_(switch), boththe component of the set point velocity that is parallel to the virtualwall and the component of the set point velocity that is perpendicularto the virtual wall is parabolically scaled based on a distance from thevirtual wall. Likewise, when the set point is located between f_(switch)and f₁, the component of the set point velocity that is parallel to thevirtual continues to be parabolically scaled with distance to thevirtual wall, while the component of the set point velocity that isperpendicular to the virtual wall is not restricted or otherwise scaled.

In some embodiments, under the non-slide mode of operation, when leavingthe zone of deceleration, the overall magnitude of the velocity of theset point is constrained to a maximum velocity (V_(E)). As describedabove with regards to the restricted-sliding mode of operation, V_(E)can be dependent on the trajectory of the set point and the location ofthe set point within the deceleration zone. As also described above, anellipse can be superimposed over the set point such that a length of thesemi-minor axis of the ellipse is selected based on the distance of theset point to the virtual wall, and such that the semi-major axis of theellipse is set to 1, and such that V_(E) is constrained based on adistance between the set point and the intersection of the ellipseboundary and the set point trajectory vector. However, under thenon-slide mode of operation, the ellipse can transition between a fixedsemi-major axis and a shrinking semi-major axis (based on a distance tothe virtual wall or a distance to a deceleration zone boundary) at thedistance f_(switch). Such an embodiment beneficially reduces oreliminates discontinuities in motion or velocity. As noted above, insome embodiments, the exit velocity of the set point can be constrainedin other ways, for instance such that the overall magnitude of the setpoint velocity is constrained, such that only the component of the setpoint velocity parallel to the virtual wall is constrained, based on thetrajectory of the set point relative to the virtual wall, based on thedistance of the set point to the virtual wall or relative to thedistance f_(switch), or based on any other suitable factor.

Note that in the cases described above with regard to the non-slidingmode of operation, the velocity of the set point of the aerial vehicle110 cannot exceed the maximum velocity determined by the relevantvelocity scaling factor. However the velocity of the set point of theaerial vehicle 110 can be less than the maximum velocity. For example,if set point of the aerial vehicle 110 moves at a constant velocity of7.5 m/s under the conditions outlined above, its velocity will notchange until it passes the midpoint of the zone of deceleration of thevirtual wall 904 where the velocity is restricted to a maximum of 7.5m/s.

The purpose of the embodiment of the non-sliding mode of operationillustrated in FIG. 9C is to demonstrate the principles of thenon-sliding mode of operation. These same principles demonstrated withregard to the FIG. 9C embodiment can also be applied to any alternativeNFZ encountered by the aerial vehicle 110 when operating in thenon-sliding mode of operation.

ADDITIONAL CONSIDERATIONS

Throughout this specification, plural instances may implementcomponents, operations, or structures described as a single instance.Although individual operations of one or more methods are illustratedand described as separate operations, one or more of the individualoperations may be performed concurrently, and nothing requires that theoperations be performed in the order illustrated. Structures andfunctionality presented as separate components in example configurationsmay be implemented as a combined structure or component.

Similarly, structures and functionality presented as a single componentmay be implemented as separate components. These and other variations,modifications, additions, and improvements fall within the scope of thesubject matter herein.

Unless specifically stated otherwise, discussions herein using wordssuch as “processing,” “computing,” “calculating,” “determining,”“presenting,” “displaying,” or the like may refer to actions orprocesses of a machine (e.g., a computer) that manipulates or transformsdata represented as physical (e.g., electronic, magnetic, or optical)quantities within one or more memories (e.g., volatile memory,non-volatile memory, or a combination thereof), registers, or othermachine components that receive, store, transmit, or displayinformation.

As used herein any reference to “one embodiment” or “an embodiment”means that a particular element, feature, structure, or characteristicdescribed in connection with the embodiment is included in at least oneembodiment. The appearances of the phrase “in one embodiment” in variousplaces in the specification are not necessarily all referring to thesame embodiment.

Some embodiments may be described using the expression “coupled” and“connected” along with their derivatives. For example, some embodimentsmay be described using the term “coupled” to indicate that two or moreelements are in direct physical or electrical contact. The term“coupled,” however, may also mean that two or more elements are not indirect contact with each other, but yet still co-operate or interactwith each other. The embodiments are not limited in this context.

As used herein, the terms “comprises,” “comprising,” “includes,”“including,” “has,” “having” or any other variation thereof, areintended to cover a non-exclusive inclusion. For example, a process,method, article, or apparatus that comprises a list of elements is notnecessarily limited to only those elements but may include otherelements not expressly listed or inherent to such process, method,article, or apparatus. Further, unless expressly stated to the contrary,“or” refers to an inclusive or and not to an exclusive or. For example,a condition A or B is satisfied by any one of the following: A is true(or present) and B is false (or not present), A is false (or notpresent) and B is true (or present), and both A and B are true (orpresent).

In addition, use of the “a” or “an” are employed to describe elementsand components of the embodiments herein. This is done merely forconvenience and to give a general sense of the invention. Thisdescription should be read to include one or at least one and thesingular also includes the plural unless it is obvious that it is meantotherwise.

Upon reading this disclosure, those of skill in the art will appreciatestill additional alternative structural and functional designs for thedisclosed remote controller, the user interface thereof, and associatedsystems. Thus, while particular embodiments and applications have beenillustrated and described, it is to be understood that the disclosedembodiments are not limited to the precise construction and componentsdisclosed herein. Various modifications, changes and variations, whichwill be apparent to those skilled in the art, may be made in thearrangement, operation and details of the method and apparatus disclosedherein without departing from the spirit and scope defined in theappended claims.

The invention claimed is:
 1. An unmanned aerial vehicle (“UAV”),configured to: receive location information describing a geographicboundary of a polygonal no-fly zone, the polygonal no-fly zonecomprising a plurality of geographic line segments; identify a closestsegment of the plurality of geographic line segments to a location ofthe UAV; determine a first distance from the location of the UAV to aportion of the closest segment nearest to the location of the UAV;identify a second closest segment of the plurality of geographic linesegments to the location of the UAV; and determine a second distancefrom the location of the UAV to a portion of the second closest segmentto the location of the UAV; and in response to determining that any ofthe first distance and the second distance are less than a thresholddistance, maintaining a first velocity component that is parallel to theclosest segment of the plurality of geographic line segments andmodifying a second velocity component that is perpendicular to theclosest segment of the plurality of geographic line segments bymultiplying a maximum possible velocity of the UAV by a velocity scalingfactor associated with a deceleration zone width of the polygonal no-flyzone.
 2. The unmanned aerial vehicle of claim 1, further configured todo one or more of further alter the trajectory of the UAV and furtheralter the speed of the UAV based on the determined second distance. 3.The unmanned aerial vehicle of claim 2, wherein the trajectory and speedof the UAV are altered such that a component of movement of the UAVperpendicular to the closest segment is reduced to zero.
 4. The unmannedaerial vehicle of claim 1, wherein a portion of the closest segment ofthe plurality of the geographic line segments is a vertex connecting twoor more of the plurality of geographic line segments of the polygonalno-fly zone.
 5. The unmanned aerial vehicle of claim 1, wherein theclosest segment of the plurality of the geographic line segmentscomprises a portion of a convex edge of the polygonal no-fly zone. 6.The unmanned aerial vehicle of claim 1, wherein the closest segment ofthe plurality of geographic line segments and the second closest segmentof the plurality of geographic line segments are unique segments.
 7. Theunmanned aerial vehicle of claim 1, wherein the closest segment of theplurality of the geographic line segments comprises a portion of aconcave edge of the polygonal no-fly zone.
 8. The unmanned aerialvehicle of claim 7, wherein the second closest segment of the pluralityof the geographic line segments comprises a different portion of theconcave edge of the polygonal no-fly zone.
 9. A method for operating anunmanned aerial vehicle (“UAV”), comprising: receiving, by the UAV,location information describing a geographic boundary of a polygonalno-fly zone, the polygonal no-fly zone comprising a plurality ofgeographic line segments; identifying, by the UAV, a closest segment ofthe plurality of geographic line segments to a location of the UAV;determining, by the UAV, a first distance from the location of the UAVto a portion of the closest segment nearest to the location of the UAV;identifying, by the UAV, a second closest segment of the plurality ofgeographic line segments to the location of the UAV; determining, by theUAV, a second distance from the location of the UAV to a portion of thesecond closest segment to the location of the UAV; and in response todetermining that any of the first distance and the second distance areless than a threshold distance, maintaining a first velocity componentthat is parallel to the closest segment of the plurality of geographicline segments and modifying a second velocity component that isperpendicular to the closest segment of the plurality of geographic linesegments by multiplying a maximum possible velocity of the UAV by avelocity scaling factor associated with a deceleration zone width of thepolygonal no-fly zone.
 10. The method of claim 9, further comprisingfurther altering one or more of the trajectory of the UAV and the speedof the UAV based on the determined second distance.
 11. The method ofclaim 10, wherein the trajectory and speed of the UAV are altered suchthat a component of movement of the UAV perpendicular to the closestsegment is reduced to zero.
 12. The method of claim 9, wherein a portionof the closest segment of the plurality of the geographic line segmentsis a vertex connecting two or more of the plurality of geographic linesegments of the polygonal no-fly zone.
 13. The method of claim 9,wherein the closest segment of the plurality of the geographic linesegments comprises a portion of a convex edge of the polygonal no-flyzone.
 14. The method of claim 9, wherein the closest segment of theplurality of geographic line segments and the second closest segment ofthe plurality of geographic line segments are unique segments.
 15. Themethod of claim 9, wherein the closest segment of the plurality of thegeographic line segments comprises a portion of a concave edge of thepolygonal no-fly zone.
 16. The method of claim 15, wherein the secondclosest segment of the plurality of the geographic line segmentscomprises a different portion of the concave edge of the polygonalno-fly zone.